physics in polarisation of the

Yuto Minami (KEK -> Osaka University)

Eiichiro Komatsu (Max-Planck-Institut für Astrophysik)

Hunting for parity-violating

physics in polarisation of the

cosmic microwave background

a.k.a. “Cosmic Birefringence”

Credit: Y. Minami (KEK)

Yuto Minami (KEK -> Osaka U.)

The methodology papers that led to this measurement

We have been working on this for ~2 years

1.Minami, Ochi, Ichiki, Katayama, Komatsu & Matsumura, “Simultaneous determination of the cosmic birefringence and miscalibrated polarization angles from CMB experiments”, PTEP,

083E02 (2019)

• The original paper to describe the basic idea, methodology, and validation

• Assumed full-sky data

2.Minami, “Determination of miscalibrated polarization angles from observed CMB and

foreground EB power spectra: Application to partial-sky observation”, PTEP, 063E01 (2020)

• Extension to partial-sky data

3.Minami & Komatsu, “Simultaneous determination of the cosmic birefringence and

miscalibrated polarization angles II: Including cross-frequency spectra”, PTEP, 103E02 (2020)

• The complete methodology for multi-frequency data, used for analysing PR3 and PR4

4

How does the electromagnetic wave of the CMB reach us?

Now shown: The cosmological redshift due to the expansion of the Universe

How does the electromagnetic wave of the CMB reach us?

Note: rotation of the polarisation plane is massively exaggerated! ?

Cosmic Birefringence

The Universe filled with a “birefringent material”

•

If the Universe is filled with a pseudo-scalar field (e.g., an axion field) coupled to the electromagnetic tensor via a Chern-Simons coupling:

Carroll, Field & Jackiw (1990); Harari & Sikivie (1992); Carroll (1998)

Turner & Widrow (1988)

Chern-Simons term

F˜^µ⌫ = X

↵

✏^µ⌫↵

2p

gF_↵

X

µ⌫

F_µ⌫ F ^µ⌫ = 2(B · B E · E)

Parity Even Parity Odd

X F_µ⌫F˜^µ⌫ = 4B · E

•

The axion field, θ, is a “pseudo scalar”, which is parity odd;

thus, the last term in Eq.3.7 is parity even as a whole.

Cosmic Birefringence

The Universe filled with a “birefringent material”

•

If the Universe is filled with a pseudo-scalar field (e.g., an axion field) coupled to the electromagnetic tensor via a Chern-Simons coupling:

Carroll, Field & Jackiw (1990); Harari & Sikivie (1992); Carroll (1998)

Turner & Widrow (1988)

Chern-Simons term

F˜^µ⌫ = X

↵

✏^µ⌫↵

2p

gF_↵

The “Cosmic Birefringence” (Carroll 1998)

This term makes the phase velocities of right- and left-handed polarisation states

of photons different, leading to rotation of the linear polarisation direction.

Cosmic Birefringence

The effect accumulates over the distance

•

If the Universe is filled with a pseudo-scalar field (e.g., an axion field) coupled to the electromagnetic tensor via a Chern-Simons coupling:

Carroll, Field & Jackiw (1990); Harari & Sikivie (1992); Carroll (1998)

Turner & Widrow (1988)

Chern-Simons term

F˜^µ⌫ = X

↵

✏^µ⌫↵

2p

gF_↵

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= 2g

_a

Z

_tobserved

t_emission

dt ✓ ˙

The larger the distance the photon travels, the larger the effect becomes.

Motivation

Why study the cosmic birefringence?

•

The Universe’s energy budget is dominated by two dark components:

•

Dark Matter

•

Dark Energy

•

Either or both of these can be an axion-like field!

•

See Marsh (2016) and Ferreira (2020) for reviews.

•

Thus, detection of parity-violating physics in polarisation of the cosmic microwave background can transform our understanding of Dark Matter/

Energy.

10

(Simpler) Motivation

Why study the cosmic birefringence?

•

We know that the weak interaction violates parity (Lee & Yang 1956; Wu et al.

1957).

•

Why should the laws of physics governing the Universe conserve parity?

•

Let’s look!

12

Credit: ESA

Foreground-cleaned Emitted 13.8 billions years ago

ESA’s Planck

Credit: ESA

Foreground-cleaned Emitted 13.8 billions years ago

ESA’s Planck

E- and B-mode decomposition of linear polarisation

Concept defined in Fourier space

•

^E-mode：Polarisation directions are parallel or perpendicular to the wavenumber direction

•

^B-mode：Polarisation directions are 45 degrees tilted w.r.t the wavenumber direction

14

Direction of the Fourier wavenumber vector

Seljak & Zaldarriaga (1997); Kamionkowski, Kosowsky & Stebbins (1997)

IMPORTANT”: These “E and B modes” are jargons in the CMB community, and completely unrelated to the electric and magnetic fields of the electromagnetism!!

Parity Flip

E-mode remains the same, whereas B-mode changes the sign

•

Two-point correlation functions invariant under the parity flip are

• The other combinations <TB> and <EB> are not invariant under the parity flip.

• We can use these combinations to probe parity-violating physics (e.g., axions)

Seljak & Zaldarriaga (1997); Kamionkowski, Kosowsky & Stebbins (1997)

Power spectrum, explained

Power Spectra

A lot have been measured

•

This is the typical figure that you find in many talks on CMB.

•

The temperature power spectrum and the E- and B-mode

polarisation power spectra have been measured well.

•

Our focus is the EB power

spectrum, which is not shown here.

Temperature anisotropy (sound waves)

E-mode

(sound waves)

B-mode (lensing) B-mode

(Gravitational Wave)

EB correlation from the cosmic birefringence

E <-> B conversion by rotation of the linear polarisation plane

•

The intrinsic EE, BB, and EB power spectra 13.8 billion years ago would yield the observed EB as

Lue, Wang & Kamionkowski (1999); Feng et al. (2005, 2006); Liu, Lee & Ng (2006)

<latexit sha1_base64="910OSkLqtnmy1k8Fk2NJltHkYrg=">AAACLXicbZDLSgMxFIYzXmu9VV26CRahgpYZqehGKK0FlxVsK3RqyaRnbDCTGZKMUIZ5ITe+igguKuLW1zC9KN4OBD7+/xxOzu9FnClt20NrZnZufmExs5RdXlldW89tbDZVGEsKDRryUF55RAFnAhqaaQ5XkQQSeBxa3m115LfuQCoWiks9iKATkBvBfEaJNlI3d1btusD5dVKr7CeuDHDoqTTFp9j1JaHOYeHLr6UHn1yppHuuYqJQcj3QZK+by9tFe1z4LzhTyKNp1bu5J7cX0jgAoSknSrUdO9KdhEjNKIc068YKIkJvyQ20DQoSgOok42tTvGuUHvZDaZ7QeKx+n0hIoNQg8ExnQHRf/fZG4n9eO9b+SSdhIoo1CDpZ5Mcc6xCPosM9JoFqPjBAqGTmr5j2iYlJm4CzJgTn98l/oXlYdI6K9kUpX65M48igbbSDCshBx6iMzlEdNRBF9+gRDdGL9WA9W6/W26R1xprObKEfZb1/ACiKpts=</latexit>

C

_`^EB,obs

= 1

2 (C

_`^EE

C

_`^BB

) sin(4 )

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+C

_`^EB

cos(4 )

• Traditionally, one would find β by fitting C

lEE,CMB

– C

lBB,CMB

to the observed C

lEB,obs

using the best-fitting CMB model, and assuming the intrinsic EB to vanish, C

lEB

=0.

•

How do we infer β from the observational data?

18

Searching for the birefringence

Improvement #1 (Zhao et al. 2015)

•

If we look at how EE and BB spectra are also modified,

•

^{We find}

•

^Thus, <latexit sha1_base64="910OSkLqtnmy1k8Fk2NJltHkYrg=">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</latexit>

C

_`^EB,obs

= 1

2 (C

_`^EE

C

_`^BB

) sin(4 )

<latexit sha1_base64="hpnvjz53moKGSW47Mmmx7UGiDtA=">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</latexit>

= 1

2 (C

_`^EE,obs

C

_`^EE,obs

) tan(4 ) + C

_`^EB

cos(4 )

No need to assume a model

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C_{`</sub><sup>EE,obs</sup> = C<sub>`}^EE cos²(2 ) + C_{`</sub><sup>BB</sup> sin<sup>2</sup>(2 ) C<sub>`}^BB,obs = C_{`</sub><sup>EE</sup> sin<sup>2</sup>(2 ) + C<sub>`}^BB cos²(2 )

<latexit sha1_base64="IJuJCTE1N6kUusDX9hjw6FJU+kI=">AAACAXicbVBNS8NAEN3Ur1q/ol4EL8EiVISSSEWPpUXwWMF+QBPDZjttl242YXcjlFAv/hUvHhTx6r/w5r9x2+ag1QcDj/dmmJkXxIxKZdtfRm5peWV1Lb9e2Njc2t4xd/daMkoEgSaJWCQ6AZbAKIemoopBJxaAw4BBOxjVp377HoSkEb9V4xi8EA847VOClZZ88+C07rvA2F16VZu4JJKlihuAwie+WbTL9gzWX+JkpIgyNHzz0+1FJAmBK8KwlF3HjpWXYqEoYTApuImEGJMRHkBXU45DkF46+2BiHWulZ/UjoYsra6b+nEhxKOU4DHRniNVQLnpT8T+vm6j+pZdSHicKOJkv6ifMUpE1jcPqUQFEsbEmmAiqb7XIEAtMlA6toENwFl/+S1pnZee8bN9UitVaFkceHaIjVEIOukBVdI0aqIkIekBP6AW9Go/Gs/FmvM9bc0Y2s49+wfj4BhFLlgA=</latexit>

+C

_`^EB

cos(4 )

<latexit sha1_base64="hjpgDlCA1j3OvcMR57Y1OklL/pA=">AAACAXicbVBNS8NAEN3Ur1q/ol4EL8Ei1IMlkYoeS4vgsYL9gCaGzXbaLt1swu5GKKFe/CtePCji1X/hzX/jts1Bqw8GHu/NMDMviBmVyra/jNzS8srqWn69sLG5tb1j7u61ZJQIAk0SsUh0AiyBUQ5NRRWDTiwAhwGDdjCqT/32PQhJI36rxjF4IR5w2qcEKy355sFp3XeBsbv0qjZxJeWlihuAwie+WbTL9gzWX+JkpIgyNHzz0+1FJAmBK8KwlF3HjpWXYqEoYTApuImEGJMRHkBXU45DkF46+2BiHWulZ/UjoYsra6b+nEhxKOU4DHRniNVQLnpT8T+vm6j+pZdSHicKOJkv6ifMUpE1jcPqUQFEsbEmmAiqb7XIEAtMlA6toENwFl/+S1pnZee8bN9UitVaFkceHaIjVEIOukBVdI0aqIkIekBP6AW9Go/Gs/FmvM9bc0Y2s49+wfj4BhxXlgc=</latexit>

C_`^EB sin(4 )

<latexit sha1_base64="Vpo7VpGoPmGR0Y3QiCM+efALLgU=">AAACAXicbVBNS8NAEN3Ur1q/ol4EL8EiVISSSEWPpUXwWMF+QBPDZjttl242YXcjlFAv/hUvHhTx6r/w5r9x2+ag1QcDj/dmmJkXxIxKZdtfRm5peWV1Lb9e2Njc2t4xd/daMkoEgSaJWCQ6AZbAKIemoopBJxaAw4BBOxjVp377HoSkEb9V4xi8EA847VOClZZ88+C07rvA2F16VZu4kvJSxQ1A4RPfLNplewbrL3EyUkQZGr756fYikoTAFWFYyq5jx8pLsVCUMJgU3ERCjMkID6CrKcchSC+dfTCxjrXSs/qR0MWVNVN/TqQ4lHIcBrozxGooF72p+J/XTVT/0kspjxMFnMwX9RNmqciaxmH1qACi2FgTTATVt1pkiAUmSodW0CE4iy//Ja2zsnNetm8qxWotiyOPDtERKiEHXaAqukYN1EQEPaAn9IJejUfj2Xgz3uetOSOb2Ue/YHx8AxkhlgU=</latexit>

+C_`^EB sin(4 )

<latexit sha1_base64="xFQX4OYFonzzXQhVgERGeHlHvOo=">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</latexit>

C_{`</sub><sup>EE,obs</sup> C<sub>`}^BB,obs = (C_{`</sub><sup>EE</sup> C<sub>`}^BB ) cos(4 ) 2C_`^EB sin(4 )

The Biggest Problem:

Miscalibration of detectors

20

Impact of miscalibration of polarisation angles

•

Is the plane of linear polarisation rotated by the genuine cosmic birefringence effect, or

simply because the polarisation-sensitive directions of detectors are rotated with respect to the sky coordinates (and we did not know it)?

•

If the detectors are rotated by α, it seems that we can measure only the

sum α+β

^.

OR

Polarisation-sensitive detectors on the focal plane

rotated by an angle “α”

(but we do not know it)

α

Wu et al. (2009); Komatsu et al. (2011); Keating, Shimon & Yadav (2012)

Cosmic or Instrumental?

The past measurements

The quoted uncertainties are all statistical only (68%CL)

•

α+β = –6.0 ± 4.0 deg (Feng et al. 2006)

•

α+β = –1.1 ± 1.4 deg (WMAP Collaboration, Komatsu et al. 2009; 2011)

•

α+β = 0.55 ± 0.82 deg (QUaD Collaboration, Wu et al. 2009)

•

^…

•

α+β = 0.31 ± 0.05 deg (Planck Collaboration 2016)

•

α+β = –0.61 ± 0.22 deg (POLARBEAR Collaboration 2020)

•

α+β = 0.63 ± 0.04 deg (SPT Collaboration, Bianchini et al. 2020)

•

α+β = 0.12 ± 0.06 deg (ACT Collaboration, Namikawa et al. 2020)

•

α+β = 0.09 ± 0.09 deg (ACT Collaboration, Choi et al. 2020)

22

first measurement

} Why not yet

discovered?

The past measurements

Now including the estimated systematic errors on α

•

β = –6.0 ± 4.0 ± ?? deg (Feng et al. 2006)

•

β = –1.1 ± 1.4 ± 1.5 deg (WMAP Collaboration, Komatsu et al. 2009; 2011)

•

β = 0.55 ± 0.82 ± 0.5 deg (QUaD Collaboration, Wu et al. 2009)

•

^…

•

β = 0.31 ± 0.05 ± 0.28 deg (Planck Collaboration 2016)

•

β = –0.61 ± 0.22 ± ?? deg (POLARBEAR Collaboration 2020)

•

β = 0.63 ± 0.04 ± ?? deg (SPT Collaboration, Bianchini et al. 2020)

•

β = 0.12 ± 0.06 ± ?? deg (ACT Collaboration, Namikawa et al. 2020)

•

β = 0.09 ± 0.09 ± ?? deg (ACT Collaboration, Choi et al. 2020)

Uncertainty in the calibration

of α has been the major

limitation

The Key Idea: The polarised Galactic foreground emission as a calibrator

24

Credit: ESA

Directions of the magnetic field inferred from polarisation of the thermal dust emission in the Milky Way

Emitted “right there” - it would not be affected by the cosmic

birefringence.

Polarised dust emission within our Milky Way!

ESA’s Planck

Searching for the birefringence

Improvement #2 (Minami et al. 2019)

•

Idea: Miscalibration of the polarization angle α rotates both the foreground and CMB, but β affects only the CMB.

•

^Thus,

measured known accurately

Key: No explicit modelling of the foreground EE and BB is necessary

26

Emitted 13.8 billions years ago

But the source of foreground is much closer!

noise

Assumption for the baseline result

What about the intrinsic EB correlation of the foreground emission?

•

For the baseline result, we ignore the intrinsic EB correlations of the foreground and the CMB .

•

The latter is justifiable but the former is not. We will revisit this important issue at the end.

Likelihood for the simplest case

Single-frequency case, full sky data

Minami et al. (2019)

28

•

We determine α and β simultaneously from this likelihood.

•

We first validate the algorithm using simulated data.

•

For analysing the Planck data, we use the multi-frequency likelihood developed in Minami and Komatsu (2020a).

How does it work?

Simulation of future CMB data (LiteBIRD)

•

When the data are dominated by CMB, the sum of two

angles, α+β, is determined precisely.

•

This is the diagonal line.

•

The foreground determines α with some uncertainty,

breaking the degeneracy.

Then σ(β) ~ σ(α) because σ(α+β) << σ(α).

•

When the data are dominated by the foreground, it can

determine α but not β due to the lack of sensitivity to the CMB.

Minami et al. (2019)

(CMB-dominated)

(Dust-dominated)

Application to the Planck Data (PR3)

lmin = 51, lmax = 1500 (the same as those used by the Planck team)

•

Planck High Frequency Instrument (HFI) data (100, 143, 217, 353 GHz)

•

Measure power spectra from “Half Missions” (HM1, HM2)

•

Mask (using NaMaster [Alonso et al.], apodization by “Smooth” with 0.5 deg)

•

Bright CO regions, Bright point sources, Dead pixels

•

I -> P leakage due to the beam is corrected using QuickPol

•

It does not change the result even if we ignore this correction: good news!

30

Information for experts

Minami & Komatsu (2020b)

100 GHz, HM2 143 GHz, HM2

217 GHz, HM2 353 GHz, HM2

Validation by FFP10

FFP10 = Planck team’s “Full Focal Plane Simulation”

•

There are 4 αν’s and one β

•

10 simulations, no foreground is included because of the treatment of the beam

•

α-only fit:

•

β-only fit:

•

No bias found. The test passed.

32

Minami & Komatsu (2020b)

Main Results

β > 0 at 2.4σ

•

^{All αν}’s are consistent with zero either

statistically, or within the ground calibration error of 0.28 deg.

•

Removing 100 GHz did not change β

•

β=0.35 deg also agrees well with the Planck determination assuming αν=0:

•

^β(αν=0) = 0.29 ± 0.05 (stat. from EB) ± 0.28 (syst.) [Planck Int. XLIX]

αν=0

0.289 ± 0.048

Minami & Komatsu (2020b)

34

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` ( C EE ` C BB ` )[ µ K 2 ] _•

Can we see β = 0.35

± 0.14 deg by

eyes?

• First, take a look at the observed EE–BB spectra.

• Black: Total

• Blue: The best-fitting CMB model

• The difference is due to the FG (and potentially systematics)

rotated only

by α rotated by α+β

Minami & Komatsu (2020b)

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` C

EB `

[ µ K

2

]

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` C

EB `

[ µ K

2

]

•

Can we see β = 0.35

± 0.14 deg by eyes?

•

Red: The signal attributed to the miscalibration angle, αν

•

Blue: The signal attributed to the cosmic birefringence, β

•

Red + Blue is the best-fitting model for explaining the data points

How about the foreground EB?

•

If the intrinsic foreground EB power spectrum exists, our method interprets it as a miscalibration angle α.

•

Thus, α -> α+γ, where γ is the contribution from the intrinsic EB.

•

The sign of γ is the same as the sign of the foreground EB.

•

From FG: α+γ. From CMB: α+β.

•

Thus, our method yields β–γ = 0.35 ± 0.14 deg.

•

There is evidence for the dust-induced TEdust > 0 and TBdust > 0. Then, we’d expect EBdust > 0, i.e., γ>0. If so, β increases further…

36

Minami et al. (2019); Minami & Komatsu (2020b)

Implications

What does it mean for your models of dark matter and energy?

•

When the Lagrangian density includes a Chern-Simons coupling between a pseudo scalar field and the electromagnetic tensor given by

•

The birefringence angle is

•

Our measurement yields

φ

LSS

φ

obs

+δφ

obs

Minami & Komatsu (2020b)

Conclusion

β = 0.35 ± 0.14 (68%CL)

•

We perfectly understand what 2.4σ means!

•

“Important, if true” (David Spergel)

•

Higher statistical significance is need to confirm this signal.

•

Our new method finally allowed us to make this “impossible” measurement, which may point to new physics.

•

Our method can be applied to any of the existing and future CMB experiments.

•

The confirmation (or otherwise) of the signal should be possible immediately.

•

If confirmed, it would have important implications for dark matter/energy.

38

β = 0.35 ± 0.14

Back-up Slides

Likelihood

Partial-sky, Multi-frequency extension

•

^where

40

Minami & Komatsu (2020a)

Likelihood

Partial-sky, Multi-frequency extension

•

^where

•

^with

Minami & Komatsu (2020a)

Likelihood

Partial-sky, Multi-frequency extension

•

^where

•

^with

Minami & Komatsu (2020a)

42